Mr Humphrys, who presents Radio 4's Today, and Mr Paxman, who hosts Newsnight on BBC2, have hit out at plans to slash costs, claiming they will undermine news and current affairs programmes.

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Sir Michael said: "The public debate, they are best to stay out of.

"There is a very difficult balance to be struck. We live in a country which prides itself on the quality of

its debate. However, in most companies you would not have staff openly debating strategy and whether it is right. To say it is untidy is perhaps an understatement."

Sir Michael also hinted that the situation could compromise the BBC's impartiality after he was interviewed on the Today programme about the cuts by Mr Humphrys, who had already aired his own view on the plans.

He added: "It was slightly complicated because John had already expressed a view on the cuts."

Mr Humphrys had said the BBC should close BBC3 or BBC4 rather than slash news and current affairs. Mr Paxman originally urged against the cuts in his speech at the Edinburgh TV Festival in August.

The presenters then turned on each other after Mr Humphrys claimed the Today programme was more important than Newsnight.

Yesterday it was revealed that some of Radio 2 and Radio 4's bestknown presenters are to hand a letter to the BBC Trust against cuts to the BBC radio newsroom.

Corrie Corfield, Charlotte Green, Susan Rae, Brian Perkins, Peter Donaldson and Rory Morrison are among more than 70 who are protesting.

Last week senior BBC figures including Newsnight presenter Gavin Esler and Today presenter Jim Naughtie signed an open letter expressing 'dismay' over the 'salami slicing' of their budgets.

Unions say strikes are virtually inevitable in the run-up to Christmas and could take programmes off air.

The cuts are aimed at plugging a £2billion shortfall caused by a lower than expected licence fee settlement with the Government.

More than one in five BBC News journalists could lose their jobs amid an increase in the use of repeats.

But Sir Michael said yesterday: "The job of the BBC is not to protect the job of everyone who works for it."